#include<iostream> #include<algorithm> #include<cstring> #include<ctime> #define timeMS (clock()*1000/CLOCKS_PER_SEC) int clk; using namespace std; #define int long long inline int read(){ int i=getchar(),r=0; while(i<'0'||i>'9')i=getchar(); while(i>='0'&&i<='9')r=(r<<1)+(r<<3)+(i^48),i=getchar(); return r; } const int N=1<<17,P=1000000007; inline int fpow(int a,int b=P-2){ int c=1; for(;b;b>>=1,a=a*a%P)if(b&1)c=c*a%P; return c; } class bst{ public: int sum1[N],sum2[N]; bst(){memset(sum1,0,sizeof(sum1));memset(sum2,0,sizeof(sum2));} void add(int p, int x){for(int i=p;i<N;i+=i&-i)sum1[i]=(sum1[i]+x)%P,sum2[i]=(sum2[i]+x*p)%P;} void add(int l,int r,int x){add(l,x),add(r+1,-x);} int ask(int p){int res=0;for(int i=p;i;i-=i&-i)res=(res+(p+1)*sum1[i]-sum2[i])%P;return res;} int get_sum(int l, int r){return (ask(r)-ask(l-1))%P;} }ds1,ds2; int n,head[N],to[N<<1],nex[N<<1],l[N],r[N],ilen[N],prd=1; int siz[N]; bool vis[N]; int ans=0; void init(){ cin>>n; for(int i=1;i<=n;i++){ l[i]=read(); r[i]=read(); prd=prd*(r[i]-l[i]+1)%P; ilen[i]=fpow(r[i]-l[i]+1); } for(int i=1;i<n;i++){ int u=read(),v=read(); to[i<<1]=v; nex[i<<1]=head[u]; head[u]=i<<1; to[i<<1|1]=u; nex[i<<1|1]=head[v]; head[v]=i<<1|1; } } int get_siz(int nd,int fa){ siz[nd]=1; for(int i=head[nd];i;i=nex[i])if(!vis[to[i]]&&to[i]!=fa)siz[nd]+=get_siz(to[i],nd); return siz[nd]; } int barycenter(int nd,int clk,int fa){ int mx=clk-siz[nd]; for(int i=head[nd];i;i=nex[i])if(!vis[to[i]]&&to[i]!=fa)mx=max(mx,siz[to[i]]); if(mx*2<=clk)return nd; for(int i=head[nd];i;i=nex[i])if(!vis[to[i]]&&to[i]!=fa){ int x=barycenter(to[i],clk,nd); if(x)return x; } return 0; } void calc(int nd,int dis,int fa){ ans=(ans+(ds1.get_sum(l[nd],r[nd])*dis+ds2.get_sum(l[nd],r[nd]))%P*ilen[nd])%P; for(int i=head[nd];i;i=nex[i])if(!vis[to[i]]&&to[i]!=fa)calc(to[i],dis+1,nd); } void add(int nd,int dis,int fa){ ds1.add(l[nd],r[nd],ilen[nd]); ds2.add(l[nd],r[nd],dis*ilen[nd]%P); for(int i=head[nd];i;i=nex[i])if(!vis[to[i]]&&to[i]!=fa)add(to[i],dis+1,nd); } void clear(int nd,int dis,int fa){ ds1.add(l[nd],r[nd],-ilen[nd]); ds2.add(l[nd],r[nd],-dis*ilen[nd]%P); for(int i=head[nd];i;i=nex[i])if(!vis[to[i]]&&to[i]!=fa)clear(to[i],dis+1,nd); } void solve(int nd){ nd=barycenter(nd,get_siz(nd,0),0); vis[nd]=true; ds1.add(l[nd],r[nd],ilen[nd]); for(int i=head[nd];i;i=nex[i])if(!vis[to[i]]){ calc(to[i],1,nd); add(to[i],1,nd); } clear(nd,0,0); for(int i=head[nd];i;i=nex[i])if(!vis[to[i]])solve(to[i]); } signed main(){ // freopen("route.in","r",stdin); // freopen("ex_route6.in","r",stdin); // freopen("route.out","w",stdout); init(); solve(1); cout<<(ans+P)%P*prd%P; // cerr<<endl<<timeMS<<' '<<clk; return 0; }